Hello Jen:

First, for ANOVA, the 3dANOVA3 -type 5 "crossed-nested" model is appropriate,
since you have fixed factor A (Group), fixed factor B (Task), and random factor
C (Subject) nested within factor A. By saying that factor C is "nested" within
factor A, we mean that Subject #7 in Group #1 for Task #1 is the same as
Subject #7 in Group #1 for Task #2 (and Task #3, and Task #4). However,
Subject #7 in Group #1 is NOT the same as Subject #7 in Group #2 (at any Task).
Using 3dANOVA3 -type 5 model, you can test for factor A (Group) main effect,
factor B (Task) main effect, and AxB (Group x Task) interaction.

The 3dANOVA2 -type 3 "mixed effects" model with fixed factor A (Task) and
random factor B (Subject) is NOT appropriate for comparing across Groups,
since Subject #7 in Group 1 is different from Subject #7 in Group 2. Also,
I don't see how you would indicate Group membership using that model.

Returning to 3dANOVA3: For technical reasons, the "-xdiff" option for
performing a t-test across individual cells is not available with the -type 5
model. By performing the t-test external to 3dANOVA3, you are sacrificing
some statistical power, since the measurement variance is estimated using only
the datasets that you input for that t-test (i.e., fewer DOF). For example, if
you perform a t-test between Groups for Task #3, the measurement variance is
estimated only from the data collected for Task #3. On the other hand, this
does avoid making the assumption that variance is constant across all of the
different Tasks. So, there is something to be said for this approach.

Doug Ward